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Math Help - trying to understand an n power algebraic formula!

  1. #1
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    trying to understand an n power algebraic formula!

    Hello,

    does anyone know why:

    [(n+3)/n]^n = [(n+3)/(n+2)]^n * [(n+2)/(n+1)]^n *[(n+1)/n]^n

    I try but no success.

    Thank you guys!
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  2. #2
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    \displaystyle \begin{align*} \left(\frac{n+3}{n+2}\right)^n \cdot \left(\frac{n+2}{n+1}\right)^n \cdot \left(\frac{n+1}{n}\right)^n &= \frac{(n+3)^n}{(n+2)^n}\cdot\frac{(n+2)^n}{(n+1)^n  }\cdot\frac{(n+1)^n}{n^n} \\ &= \frac{(n+3)^n\cdot (n+2)^n\cdot (n+1)^n}{(n+2)^n \cdot (n+1)^n \cdot n^n} \\ &= \frac{(n+3)^n}{n^n} \\ &= \left(\frac{n+3}{n}\right)^n\end{align*}
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  3. #3
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    You are the man!

    Thank you very very much for your help!
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